store brands and store competition

7/28/2019 Store Brands and Store Competition

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6th Global Conference on Business & Economics ISBN : 0-9742114-6-X

Store Brands and Store Competition

Dr. Sungchul Choi, School of Business, University of Northern British Columbia, Canada

Dr. Karima Fredj, Economics Program, University of Northern British Columbia, Canada

ABSTRACT

Most past studies of store brands ignored store competition and focused on limited interactions

among channel members. This research seeks to extend the literature in this area by considering various channel

leadership structures and retail competition in a channel of a single national brand manufacturer and two competing

store brand retailers that also sell the national brand. Besides the variety in vertical price leadership between the

national brand manufacturer and the store brand retailers, we particularly investigate the role of horizontal price

leadership between two store brand retailers.

We find that the two competing retailers are better-off when they practice price leadership between them.


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of Agriculture (USDA) 2000's estimates, one out of every five items sold per day in the U.S. supermarkets, drug

chains and mass merchandisers is a store brand product. Because of such success of store brands in several product

categories over the past two decades, competition between national brands and store brands has been extensively

studied.

One research stream focuses on the empirical approach that investigates the effects of some variables such

as advertising, perceived quality, and industry concentration on competition between national brands and store

brands to explain the variation in store brand market share across different product categories (see for example;

Cannor and Peterson 1992, Hoch and Banerji 1993, Hoch 1996, Kim and Parker 1999, Cotterill et al. 2000).

Another research stream introduces theoretical models that describe price competition between national

brands and store brands to study some related issues. For instance, Raju et al. (1995) developed a game-theoretic

model in order to examine the conditions under which it is profitable to introduce store brands; Narasimhan and

Wilcox (1998) examined the incentives for store brand introduction in the loyal/switcher market structure; and more

recently, Sayman et al. (2002), Du et al. (2004), and Choi and Coughlan (2006) investigated the retailer's store brand

positioning issue.

However, the existing literature of price competition in economics-based modeling between national brands

and store brands still has its limitations and our main contribution in this paper is to address some of them.


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composed of one national brand manufacturer and two retailers who sell their own store brand in addition to

marketing the manufacturer's national brand.

Secondly, previous studies, related to store brands issues, only investigated the Manufacturer Stackelberg

(MS) channel leadership structure where manufacturers are modeled as Stackelberg leaders and retailers as

followers (see for example; Raju et al. 1995, Narasimhan and Wilcox 1998, Sayman et al. 2002). This excludes

some other possible channel leadership structures that have been proven pertinent by the previous literature that did

not account for store brand competition; such as a Vertical Nash (VN) where manufacturers and retailers are at the

same power level, or Retailer Stackelberg (RS) where, as opposed to the MS, retailers act as price leaders and

manufacturers as price followers. Indeed, as argued in this literature, in certain circumstances retailers may be

"powerful" enough to lead the channel, leaving manufacturers no other choice but to accordingly adjust their

decisions (Lee and Staelin 1997). These retailers are often much larger than most of the manufacturers, and exercise

their power on the flow of products (Choi 1996). This is exemplified in the real world by the dominance of large

retailers such as Wal-Mart (Choi 1991, Lee and Staelin 1997). Henceforth, we believe that considering all the

different leadership structures would particularly reflect the impact of store brands on the strategic role of retailers in

the channel (Trivedi 1998).

Finally, existing studies in this area ignored horizontal price leadership by assuming that channel members


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In summary, the primary focus of this paper is to investigate price competition between a manufacturers

national brand and retailers store brands in the presence of store competition. As indicated above, this paper

extends the previous literature mainly in three directions: (1) considering both product and store differentiation, (2)

applying different vertical price leadership structures (MS, RS and VN), to a store brand model and (3) applying

horizontal price leadership at the retail level.

This paper is organized as follows. In the next section, we develop a model that examines price

competition between a national brand and store brands in a channel structure with one manufacturer and two

retailers. In the third section, we derive the analytical equilibrium solutions for the prices, margins, quantities

demanded and profits under the different channel leadership structures. In the fourth section, we perform sensitivity

analyses, comparisons and discuss the implications of the channel leadership. Finally, we conclude and delineate

further research directions.

THE MODEL

This section describes the demand and profit functions and provides a description of the channel leadership

structures.

We assume that the manufacturer produces a national brand product that he distributes to two competing


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)()(1(22

1imiim jmimim p p p p pq +++

=

(1)

))((22

1iimii p p pq ++

=

, (2)

where:m the index for the manufacturer,

:,2,1, ji ji = indexes for the retailers,:imq the demand of the manufacturers national brand at store i,

:iq the demand of the store is brand,:im p the retail price of the manufacturers national brand at store i,

:i p the retail price of the store is brand,: the cross price sensitivity between the national brand and a store brand at store i,: the cross price sensitivity between the two stores for the national brand,: the store brands base level of demand.

Smaller values of indicate less product substitutability (or more product differentiation) between the

national brand and a store brand. A small value of the cross-price sensitivity between two products hence implies

that a change in the price of one of the products will have small impact on the demand of the other product and vice-

versa. By considering the same between the national brand and each of the store brands, we implicitly assume that

the national brand is symmetrically positioned with respect to the two store brands.

A smaller value of , on the other hand, represents less store substitution (or more store differentiation)

implying that price differences for the same national brand between the two stores has less impact on the demand


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structures from the effects of cost difference, we assume zero marginal costs without loss of generality. The profit

function for a national brand manufacturer can then be written as:

( ) ==

==2,12,1 i

mimi

mimm qwqw (3)

and the profit function for each retailer is

iimii R q pqmi += , (4)

where mw is the national brand manufacturers wholesale price, mimi w pm = is the store is margin on the

national brand. 2

The Channel Leadership Structure

To model variety in price leadership among channel members, we consider both vertical interactions between the

manufacturer and the retailers, and horizontal interactions between the two retailers. In addition, at each interaction

level, we consider both simultaneous and sequential plays, which translate into the following four pricing games:

The Manufacturer Stackelberg (MS): It refers to a Stackelberg price leadership at the vertical level

(where the manufacturer is the leader and retailers are followers) and a simultaneous Nash game between the two


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The Retailer Stackelberg (RS): It also refers to a Stackelberg price leadership but as opposed to the

MS, the manufacturer is the follower and retailers are the leaders. Solved backward, this means that the

manufacturer first solves for the wholesale price of the national brand that maximizes his profits. The obtained

reaction function is then used by the retailers while simultaneously maximizing their respective profits.

The Retailer Double Stackelberg (RDS): This game is similar to the RS in terms of the vertical

interaction between the manufacturer and the retailers. However, it differs at the horizontal level, by considering

sequential interaction la Stackelberg rather than a simultaneous one la Bertrand-Nash between the two retailers.

Thus, one retailer (Retailer 2 in our model) has price leadership over the other (Retailer 1). Solved backward, this

means that the manufacturer first chooses his wholesale price. Then the following retailer (Retailer 1) chooses her

margins for the national brand and her store brand before the leading retailer (Retailer 2), using the reaction

functions of the two other channel members, fixes the margins for the national brand and her store brand that

maximize her profits.

Figure 1 illustrates these different configurations of the channel leadership structures. As mentioned in the


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Figure 1. The Channel Leadership Structure

(a) Manufacturer Stackelberg (MS) (b) Retailer Stackelberg (RS)

(c) Vertical Nash (VN) (d) Retailer Double Stackelberg (RDS)

Retailer 2Retailer 1

Manufacture


Manufacture


Manufacture Retailer 2

Retailer 1

Manufacturer


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24)12(1

+++

+++=

MS m MS

iwm , and

)24(2)22(2

+++

++++=

MS m MS

i

w p .

It is interesting to notice from these expressions that as the wholesale price of the national brand goes up,

each retailer decreases her margin on the national brand and increases the price of her store brand. This means that a

high wholesale price of the national brand results in a lower retail margin on the product, for which the retailers can

compensate by choosing higher retail margin on their own store brand.

Substituting these reaction functions into the manufacturer profit function (equation 3) and maximizing it

with respect to the wholesale price gives the following optimal value:

))12)(1(2)24((2))1(12(2

2 +++++

++++=

MS

mw .

Finally, replacing this value of MS mw in the retailers reaction functions yields the optimal control

variables values for each retailer i=1,2:

))62420()52832()32(2)4((2)2)(34()1)(4(2)1)(2(6)1(2

222223

32

++++++++++

++++++++++= MS

im and


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2,1;24

)12(1 =+++

+++= i

wm

VN mVN

i

,

2,1;)24(2

)22(2=

+++

++++= i

w p

VN mVN

i

and

)1(4

))(1()(2 2121+

++++=

VN VN VN VN VN m

mm p pw .

The optimal solutions are then obtained from solving the above system:

2,1;)23)(2()12)(1(6

)1(3)234( 2 =+++++

++++= im VN i

,

2,1;)23)(2()12)(1(6)323)(1()33( =

+++++

++++++=

i pVN

i

and

)23)(2()12)(1(6

)22()12(2+++++

++++=

VN

mw .

Th ilib i i i d fi f h h l b b il d i d b b i i h l i


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of the two products. Furthermore, the wholesale price of the national brand decreases as the retail margin of the

national brand increases ( 01

>>>>RDS p

RDS p

RS p

VN p

MS p .

iii. RDS m RDS

m RDS RDS RDS RDS p pand mm p p 121212 , >>> .

The first part of the proposition above indicates that the retail price of the national brand at each store is

always higher than the store brands price and the wholesale price of the national brand. This result holds for all

channel leadership structures and regardless of the values that the different cross-price sensitivities and base level

demand parameters can take; confirming face validity of the model.

The second part of the proposition shows that the relationship between the national brand's wholesale price

and the store brand is retail price, however, depends on the parameters of the demand function and how they relate

to each other. The way we present the results generates critical values of the base level demand of the store brand as

a function of the cross-price sensitivities between stores as well as between products. When is greater than the

critical value under each channel leadership structure, the price of a retailers store brand is higher than the

wholesale price of the national brand and vise-versa. These findings reinforce the sensitivity analysis results with

respect to . Furthermore, by comparing the different critical values obtained under the different leadership


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In sum, the last proposition aiming at comparing the prices within each leadership scenario showed that in

some cases this can be impossible to accomplish without referring to the channel leadership structure effects. We

therefore compare the equilibrium solutions obtained in the four channel leadership structures to have a better idea

of their impact on each channel members outcomes. We summarize the results in propositions (5) to (7) stated and

discussed below.

PROPOSITION 5. Every thing else remaining the same, Stackelberg channel leaders get higher unit

margins on the national brand compared to the VN game. The two competing retailers get even higher unit margins

on the national brand playing a sequential Stackelberg rather than interacting simultaneously la Bertrand-Nash.

The wholesale price of the national brand is the highest in the MS leadership, consecutively followed by

the VN, RS, and RDS cases ( RDS m RS

mVN

m MS

m wwww >>> ). In contrast, the retail margin of the national

brand at each store is the highest in the RDS case followed consecutively by the RS, VN, and MS cases (

2,1,12 =>>>> immmmmMS

iVN

i RS i

RDS RDS ). These results imply that a channel leader can obtain a higher

mark-up on the national brand, which provides a direct incentive for each channel member to become the leader. In


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The retail prices of the national brand resulting from the three different Stackelberg leadership are always

higher than those of the VN case (VN

m RS

m RDS

m MS

m p p p p 2222 >>> , DRS

m MS

m p p 11 > , andVN

m RS

m p p 11 > ). This indicates

that consumers are better-off in the absence of channel leadership, which is consistent with previous studies'

findings (Shugan and Jeuland 1988, Choi 1991 and 1996). In addition, the two retailer Stackelberg cases (RS and

RDS) lead to lower retail prices for the national brand compared to the MS case. This result also corroborates with

the previous conclusion that a manufacturers leadership results into higher retail prices than a retailers leadership

when accounting for store competition (Choi 1996). With respect to two retailers Stackelberg scenarios, the

Stackelberg price leader (Retailer 2) benefit from a higher retail price for the national brand under the RDS

compared to the RS case. The equivalent relationship is, however, undetermined for the Stackelberg follower

(Retailer 1).

The retail prices of the two store brands are also higher under the MS case compared to the VN and under

the RDS compared to the RS case ( VN i MS i p p > and 2,1, => i p p

RS i

RDS i ). The intuition behind this result

is that each retailer sets a relatively high price for her own store brand under the MS structure because the competing

national brand price is also higher in this case and chooses a high price under the RDS as she has more power under

this scenario compared to the RS. It is not clear though, from these price comparisons, that the store brand provides


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2,1, =>>> i MS RVN R RS R RDS R iiii ). These results are expected, as the leader has informational advantage

(knows the followers' reaction functions) and exploits it in his/her pricing strategy. In addition, it is confirmed once

again that the two competing retailers are better-off when there is price leadership between them as they benefit

from higher retail margins for the national brand and store brands compared to the RS case. Thus, horizontal price

leadership at the retail level would be the best pricing strategy not only for the price leader but also for the price

follower when they dominate the national brand manufacturer.

Globally, and as expected, the total channel profits ( x R x R

xm

x21 ++= ) are maximized when there is

no channel leadership. In addition, the two retailer Stackelberg cases (RS and RDS) produce larger channel profits

than the MS case ( MS RDS RS VN >>> ).

CONCLUSION

This paper presents a general analytical framework that helps better understand the nature of price competition

between national and store brands in presence of store competition. In fact, we consider both intra-store competition

between national brand and store brands and inter-store competition between two stores. In addition, we consider

various price leadership structures among the channel members, namely simultaneous interactions la Bertrand-


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The retailers' base level of store brand demand has a positive impact on both the wholesale price

and the retail margins. Its impacts on the quantities demanded of the store brand at the

equilibrium are positive. On the national brand, demand impacts are negative, resulting in lower

profits for the manufacturer.

Some other results provide new insights:

The two competing retailers benefit from price leadership at the retail level regardless of their

roles (leader or follower).

The retail prices of the national brand and store brands under the MS case are always higher than

those of the two retailer Stackelberg cases.

The total channel profits increase as the retailers have more price leadership than the national

brand manufacturer. They are also higher under the RS compared to the RDS leadership.

These findings are insightful for practitioners in many perspectives. First, powerful store brand retailers

need to seek price leadership between them as it would increase their profits in presence of store competition. As

such, a store brand retailer should not fear her competitor (second retailer) as long they dominate over the

manufacturer. Second, each store should develop a unique positioning strategy to differentiate from the competitors

as it helps in increasing the retailers profits. Finally, the retailers should offer a store brand that is a close substitute


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REFERENCES

Basuroy, S., M. K. Mantrala, R. G. Walters. 2001. The impact of category management on retailer prices and performance: Theory and evidence.

J. Marketing . 65 16-32.

Bresnahan, T. F. 1989. Industries and market power. Handbook of Industrial Organization , North-Holland, Amsterdam, The Netherlands.

Choi, S. 1996. Price competition in a duopoly common retailer channel. J .Retailing . 72 (2) 117-134.

Choi, S., A. T. Coughlan. 2006. Private label positioning: Quality versus feature differentiation from the national brand. J. Retailing . 82 (2) 79-93.

Connor, J., E. Peterson. 1992. Market structure determinants of national brand-private label price difference of manufactured food products. J.

Industrial Econom. 40 157-171

Cotterill R., B. Putsis, R. Dhar. 2000. Assessing the competitive interaction between private labels and national brands. J. Bus . 73 (1) 109-137.

Dhar, T. P., S. Ray. 2004. Understanding dynamic retail competition through the analysis of strategic price response using time series techniques.

Working paper, University of British Columbia, Vancouver, Canada.

Du, R., E. Lee, R. Staelin. 2004. Focus, fill the gap, attack, or stimulate: Retail category management strategies with a store brand. Working

paper, Duke University, Durham, NC.

Hoch, S. 1996. How should national brands think about private labels? Sloan Management Rev . 37 (2). 89-102.

Hoch, S., S. Banerjee. 1993. When do private labels succeed? Sloan Management Rev . 34(4) 57-67.

Kim, N., P. M Parker. 1999. Collusive conduct in private label markets. Internat. J. Research Marketing . 16 143-155.

Lee, E, R. Staelin. 1997. Vertical strategic interaction: Implications for channel pricing strategy. Marketing Sci . 16 (3) 185-207.

McMaster, Derek. 1987. Own brands and the cookware market. Eur. J. Marketing . 1(21) 83-94.

Narasimhan, C., R. Wilcox. 1998. Private labels and the channel relationship: A cross-category analysis. J. Bus . 71 (4) 573-600.

Raju J S Dhar R Sethuraman 1995 The introduction and performance of store brands Management Sci 41 (6) 957 978


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APPENDIX

Table 1 Equilibrium Outcomes

(a) The MS case

wm

2 2 1 2 4 6 4

mi2 1 6 2 2 1 2 3 4 1 4 3 2

2 3 4 2 2 2 3 2 2 32 28 5 2 20 24 6 2

pim wm mi2 3 4 2 2 3 4 1 2 2 2 4 7 3 2 9 5 2 4 4 6 24 5

2 2 4 2 1 2 4 6 4

pi4 2 3 2 4 3 4 1 2 2 2 3 8 3 5 4 5 7 2 4 16 2 1 4 5 18

4 3 4 2 2 2 3 2 2 32 28 5 2 20 24 6 2

qim2 1 4 2

8 2 4 1

qi4 1 2 1 6 4 2 4 8 2 3

8 2 1 2 4 6 4 1

M wm q1 m q2 m2 1 4 2 2

8 3 4 2 2 2 3 2 2 32 28 5 2 20 24 6 2 1

R imi qim pi qi ... i 1, 2

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(b) The VN case

wm2 1 4 2

6 4 3 2 4 2 9 4

mi2 3 2 1 4 3

6 4 3 2 4 2 9 4

pim wm mi2 2 3 2 1 8 3 2

6 4 3 2 4 2 9 4

pi

3 2 3 2 1 3 1 2

6 4 3 2 4 2 9 4

qim1 2 1 4 2

2 6 4 3 2 4 2 9 4 1

qi3 2 2 2 6 2 1 9 4

2 6 4 3 2 4 2 9 4 1

M wm q1 m q2 m1 2 1 4 2 2

6 4 3 2 4 2 9 4 2 1


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(c) The RS case

wm6 8 2 9 2 4 2 12 7 4

2 1 10 8 5 2 4 2 15 8

mi4 5 2 1 8 5

10 8 5 2 4 2 15 8

pim wm mi14 8 10 3 1 2 21 5 2 4 2 38 20 7 4

2 1 10 8 5 2 4 2 15 8

pi5 4 5 2 1 5 2 1 2

10 8 5 2 4 2 15 8

qim6 8 2 9 2 4 2 12 7 4

4 10 8 5 2 4 2 15 8 1

qi2 5 4 4 1 10 6 3 8 20 3 6 2 2 6 25 4 11

4 1 10 8 5 2 4 2 15 8 1

M wm

q1 m

q2 m

6 8 2 9 2 4 2 12 7 4 2

4 1 10 8 5 2 4 2 15 8 2 1


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(d) The RDS case

wm2 121 504 656 2 256 3 2 1089 128 3 12 16 2 287 13 4032 76 6 1936 22 2 87 32 8 439 76 3 287 166

2 2 3993 128 3 29 5 4 2 3233 312 13039 532 2 3 7623 16 3 288 77 20 2 937 144 2 10893 722 5 8712 8 2325 304 3 2112 998 2 11863 3424 4 15972 32 3 193 71 39638 3800 2 29437 6400

8 1 51 6 16 24 10 2 3 2 51 188 208 2 64 3 5 3672 6680 3389 2 424 3 918 3008 2912 2 768 3 2 2 1683 4853 4072 2 912 3 2 3 3213 8062 5800 2 1088 3 4 6732 14506 8831 2 1364 3

m14 41 120 80 2 51 6 16 20 5 2 1 4 328 51 96 2 5 4 210 37 4 2 1076 357 12 2 99 40 2411 888

2 3 3728 1938 4 2 776 463 7310 4103 2 4 3622 2550 3 2 749 572 6191 4572 5

3760

3264 2

1692

1519

5546

49184 51 6 16 24 10 2 3 2 51 188 208 2 64 3 5 3672 6680 3389 2 424 3 918 3008 2912 2 768 3 2 2 1683 4853 4072 2 912 3 2 3 3213 8062 5800 2 1088 3 4 6732 14506 8831 2 1364 3

m228 48 17 4 4 3 1 2 70 17 4 24 7 2 2 129 68 2 73 42 3 214 170 200 163

2 34 80 32 2 17 4 8 8 2 4 51 100 32 2 2 2 221 354 88 2 3 408 524 96 2

pim wm mi ... i 1, 2

p14 51 188 208 2 64 3 51 6 16 20 5 2 1 4 51 1 8 32 3 1 10 28 6 47 8 2 19 156

2 2 102 7 26 80 2 19 74 16 3 16 77 7 288 1057 5 82 3 1 2 816 4 5 2 1911 2558 5238 6578 4 204 25 41 3 416 996 2 5052 8311 2 4916 8703 2 3 102 19 44 8 3 45 142 2 2846 7040 4623 10675

4 3 4 3 2 2 9 8 34 80 32 2 17 4 8 8 2 4 51 100 32 2 2 2 221 354 88 2 3 408 524 96 2

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p22 17 40 16 2 17 4 4 3 1 2 17 85 8 2 1 6 2 17 80 3 14 2 1 2 34 5 7 187 262

2 34 4 9 4 2 8 23 204 451 2 34 80 32 2 17 4 8 8 2 4 51 100 32 2 2 2 221 354 88 2 3 408 524 96 2

q1 m82 240 160 2 4 123 8 2 20 3 2 150 7 4 3 246 5 81 14 2 2 72 35 2 2 533 16 2 29 9 2 535 56

4 328 8 55 14 2 129 88 16 34 80 32 2 17 4 8 8 2 4 51 100 32 2 2 2 221 354 88 2 3 408 524 96 2 1

q2 m7 12 21 4 6 2 14 11 4

16 3 4 3 2 2 9 8 1

q18 17 40 16 2 5 41 2 1 2 8 27 68 8 30 71 2 3 351 1700 4 2 45 142 4 151 622

4 8 81 272 2 208 498 4 226 675 2 27 476 32 2 1 10 68 960 4 2 81 646 4 2 16 77 170 1111

16 1 34 80 32 2 17 4 8 8 2 4 51 100 32 2 2 2 221 354 88 2 3 408 524 96 2 1

q24 3 4 3 10 24 7 1 2 5 48 8 1 6 2 15 60 2 8 23

16 1 3 4 3 2 2 9 8 1

M wm q1 m q2 m1 2 1 4 2 2

6 4 3 2 4 2 9 4 2 1


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store brands and store competition

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